Commutators Generated By Singular Integral Operators With Variable Kernels

Harmonic analysis is one of the core subjects of mathematics, which in-volves the theory of spherical harmonic function, potential theory, singular in-tegral and general differentiable function space, etc. And, the boundedness of all kinds of operators has always been one of the important subject in harmonic analysis, which is closely related to many problems.In chapter 1, we briefly introduce the background, current status about the singular integral operator with variable kernel and the fractional integral opera-tor with variable kernel, and some related notations.In chapter 2, we discuss the boundedness of the singular integral operator with variable kernel on the generalized local Morrey spaces, as well as the boundedness of the commutators generated by the singular integral operator with variable kernel and local Campanato functions.In chapter 3, we discuss the boundedness for the fractional integral operator with variable kernel on the generalized local Morrey spaces, as well as the boundedness of the commutators generated by the fractional integral operator with variable kernel and local Campanato functions.